bc performance standards numeracy...bc performance standards: numeracy...

BC Performance Standards

Ministry of Education

NumeracyNumeracy

Numeracy



A C K N OW L E D G M E N T S

These materials reflect the collective wisdom of teachers throughout the province. TheMinistry of Education would like to acknowledge both the time and the expertise thathundreds of teachers contributed.

The Ministry of Education would also like to acknowledge the work of: Horizon Researchand Evaluation Inc., for facilitation of the field activities; A. Toutant Consulting Group Ltd.,for design and production; and DGB Typesetting for desktop publishing.

C A N A D I A N C ATA L O G U I N G I N P U B L I C AT I O N D ATAMain entry under title:BC performance standards. Numeracy. – – Rev. ed.

ISBN 0-7726-4835-2

1. Numeracy - Testing. 2. Mathematical ability -Testing. 3. Mathematics - Study and teaching(Elementary) - Evaluation. I. British Columbia.Ministry of Education.

QA109.B13 2002 372.7' 2' 076 C2002-960183-5

© 2002 Ministry of Education, Student Assessment and ProgramEvaluation Branch, Province of British Columbia.

C O P Y R I G H T N OT I C E

No part of this document may be reproduced in any form or by any means, includingelectronic storage, reproduction, execution or transmission without the prior writtenconsent of the Province.

P R O P R I E TA RY N OT I C E

This document contains information that is proprietary and confidential to the Province.Any reproduction, disclosure or other use of this document is expressly prohibited exceptas the Province may authorize in writing.

Permission to copy and use this publication in part, or in its entirety, for non-profiteducational purposes within British Columbia and the Yukon, is granted to all staffof BC school board trustees, including teachers and administrators; organizationscomprising the Educational Advisory Council as identified by Ministerial Order; andother parties providing direct or indirect education programs to entitled students asidentified by the School Act.

Contents

About the BC Performance Standards . . . 1

Numeracy in BC Schools . . . 9

Grade 1 . . . 13

Grade 2 . . . 49

Grade 3 . . . 77

Grade 4 . . . 97

Grade 5 . . . 121

Grade 6 . . . 151

Grade 7 . . . 187

Grade 8 . . . 217

A B O U T T H E B C P E R F O R M A N C E S T A N D A R D S○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

1

Performancestandardssupport ongoinginstruction andassessment.

About the BC PerformanceStandards

T he BC performance standards have been developed for

voluntary use in BC schools. They describe the professional

judgments of a significant number of BC educators about

standards and expectations for the following key areas of learning:

◆ reading

◆ writing

◆ numeracy

◆ social responsibility

The standards focus exclusively on performance assessment. In

performance assessment students are asked to apply the skills and

concepts they have learned to complete complex, realistic tasks.

This type of assessment supports a criterion-referenced approach

to evaluation and enables teachers, students, and parents to compare

student performance to provincial standards.

The BC performance standards are intended as a resource to support

ongoing instruction and assessment. Teachers can use these standards to:

◆ monitor, evaluate, and report on individual student performance

◆ identify students who may benefit from intervention

◆ develop a profile of a class or group of students to supportinstructional decision-making

◆ prompt discussions with parents, students, and other teachersabout student performance

◆ inform professional development activities

◆ collaboratively set goals for individuals, classes, or schools

◆ develop evidence for school growth plans

◆ provide models for designing performance tasks

B C P E R F O R M A N C E S T A N D A R D S : N U M E R A C Y○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

2



NumeracyNumeracy

The BCperformance

standardscomplement

existingcurricula and

assessmentmaterials

developed bythe Ministry

of Education.

Ongoing Development

R E F E R E N C E S E T C O N N E C T I O N

The BC performance standards are a continuation of the work begun in

the provincial reference sets.

Starting in 1991, the province developed reference sets for reading,

writing, mathematical development, group communication skills, and

problem solving. The reference sets show the broad range of possible

student development in each of these essential skill areas. They can be

used to evaluate student work in any subject.

The BC performance standards work within these same ranges of

development in the same areas. They can also be used to evaluate

these skills in any subject. However, the standards focus on levels

of performance at particular grades.

For both sets of documents, teachers used their experience and student

work to develop and validate the materials. Both also use student work

and teacher comments to illustrate and describe levels of performance.

L E A R N I N G O U TC O M E S

Learning outcomes describe what students are supposed to learn in

each subject and at each grade level. Learning outcomes are often called

content standards. Content standards answer the question: “What

knowledge, skills, and attitudes are students expected to develop at

this grade level?”

The ministry’s Integrated Resource Packages list prescribed learning

outcomes for BC provincial curricula for each subject and grade level.


3

Ongoing Development

The standardsdescribe andillustrate fourlevels ofperformance.

P E R F O R M A N C E S TA N D A R D S

Performance standards describe levels of achievement in key areas of

learning. Performance standards answer the questions: “How good is

good enough? What does it look like when a student’s work has met the

expectations at this grade level?”

The BC performance standards describe and illustrate the following four

levels of student performance in terms of prescribed learning outcomes

relevant to the key areas of reading, writing, numeracy, and social

responsibility.

N OT Y E T W I T H I N E X PE C TAT I O N S

◆ the work does not meet grade-level expectations

◆ there is little evidence of progress toward the relevant prescribedlearning outcomes

◆ the situation needs intervention

M E E T S E X PE C TAT I O N S ( M I N I M A L L E V E L )

◆ the work may be inconsistent, but meets grade-level expectationsat a minimal level

◆ there is evidence of progress toward relevant prescribedlearning outcomes

◆ the student needs support in some areas

F U L LY M E E T S E X PE C TAT I O N S

◆ the work meets grade-level expectations

◆ there is evidence that relevant prescribed learning outcomes havebeen accomplished

E XC E E D S E X PE C TAT I O N S

◆ the work exceeds grade-level expectations in significant ways

◆ the student may benefit from extra challenges


4

G R A D E 4 N U M E R A C Y○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

49

Sample 1: Conducting Surveys (Data Analysis)

C O N T E X T

This was the culminating activity in a data collection unit. During the

unit, the teacher modelled and provided several opportunities for

students to practise matching questions to a sample population,

collecting data, and constructing and analyzing graphs.

M AT H E M AT I C A L C O N C E P T S

◆ select appropriate sample or population

◆ collect first- and second-hand data

◆ create interval graphs/tables

◆ construct bar graphs

◆ evaluate data collection processes

P R O C E S S

The class reviewed what they had learned about conducting surveys

and communicating the results. The teacher explained that for this

survey, each student would choose his or her own question and work

independently to collect and display the data. The class brainstormed

some possible questions.

Students then worked independently to:

1. Choose a survey topic.

2. Survey the sample population (usually their classmates) and tallythe results.

3. Create a bar graph to display the data collected.

4. Analyze the data: write a short summary of the results (e.g., range,most frequent choice, number of people).

5. Evaluate the survey (e.g., comment on the sample and thedata collection).

6. Post the work around the room for other students to view.

The class discussed what they had learned and commented on ways that

their projects were similar and different. They also developed a list of

“tips” for collecting and displaying data, which the teacher posted for

future reference. For the remainder of the school year, the teacher

encouraged students to look for situations where they could collect and

report on data in other subject areas.

G R A D E 4 N U M E R A C Y○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

45

Quick Scale: Grade 4 NumeracyThis Quick Scale is a summary of the criteria described in detail in the Rating Scale that follows. These criteria

may apply at any time of the year, depending when specific skills or concepts are introduced.

Aspect Not Yet Within Expectations Meets Expectations Fully Meets Expectations Exceeds Expectations(Minimal Level)

SNAPSHOT

CONCEPTS ANDAPPLICATIONS*

• recognizingmathematics

• grade-specificconcepts, skills

• patterns,relationships

STRATEGIESANDAPPROACHES

• procedures• estimates to verify

solutions

ACCURACY

• recording,calculations

The student may beunable to complete thetask without ongoinghelp; cannotfollow proceduresindependently.

• may be unable toidentify basic conceptsand procedures needed

• work is inaccurate orincomplete

• may need one-to-onesupport to identifysimple patterns andrelationships

• cannot break the taskinto stages, steps, orsections

• unable to verify resultsor solutions

• may include majorerrors in recording orcalculations

• work may be unclearand confusing

• may omit or makemajor errors in tables,charts, displays,diagrams

• may be unable toexplain proceduresand results

The work satisfies mostbasic requirements of thetask, but it is flawed orincomplete in some way.The student may needsome help.

• identifies someconcepts andprocedures needed

• applies most relevantconcepts and skillsappropriately; someerrors or omissions

• identifies simplepatterns and relation-ships if prompted (e.g.,to make predictions)

• tries to followinstructions; does notcheck or adjustprocedures

• needs help to verifyresults or solutions

• may include somerecording or calculationerrors; comparisons aregenerally reasonable

• work may be confusingin places

• includes most requiredtables, charts, displays,and diagrams; someerrors or omissions

• explanations andconclusions may beincomplete; littlemathematical language

The work is complete andaccurate (may includeminor errors). Thestudent is able todevelop a simpleextension.

• identifies concepts andprocedures needed

• applies relevantconcepts and skills;may be somewhatinefficient or makeminor errors

• identifies, explains, anduses simple patternsand relationships

• structures the tasklogically; may beinefficient

• if asked, verifies resultsor solutions

• recording andcalculations aregenerally accurate; maybe minor errors

• work is generally clear,easy to follow

• required tables, charts,graphs, and diagramsare generally accurate;minor errors oromissions

• offers logicalexplanations andconclusions; somemathematical language

The work is complete,accurate, and efficient.The student may findan alternative or ashortcut, or develop anextension.

• identifies conceptsand proceduresneeded; may proposealternative solutions

• applies relevantconcepts and skillsefficiently; precise

• identifies, explains,and uses patterns andrelationships; maynotice subtle patterns

• structures the taskefficiently

• may independentlyverify results orsolutions

• accurate recordingand calculations,including units; mayuse mental math

• work is clear and easyto follow

• required tables, charts,graphs, diagrams areaccurate and complete

• offers logicalexplanations andconclusions; usesmathematicallanguage

REPRESENTATIONANDCOMMUNICATION

• presenting work• constructing

charts, diagrams,displays

• explainingprocedures, results

* You may want to list key curriculum concepts or skills for a particular task.

_________________________________ ________________________________ _____________________________________

_________________________________ ________________________________ _____________________________________

These keycomponents are

included foreach grade

level.

Additional sample tasks, student work, and other support materials

are available at the Ministry of Education’s web site.

Key Components

Rating Scale. This is the full version of the performance standards, with

the four performance levels described in detail.

Quick Scale. This is a short-form

summary of the Rating Scale. Quick

Scales are intended for daily use.

Teachers may also want to share them

with students and parents.

Sample Tasks. These are tasks developed

by practising teachers to provide

opportunities to assess student work

in the skill area. Each sample task

includes examples of student work.

Teachers may use the tasks as given

or as models. Any tasks used should

first be reviewed for issues sensitive

to the class or community.

Fully Meets Expectations Exceeds ExpectationsAspect Not Yet Within Expectations Meets Expectations (Minimal Level)

Rating Scale: Grade 4 NumeracyThese criteria may apply at any time of the year, depending when specific skills or concepts are introduced. *

SNAPSHOT

CONCEPTS ANDAPPLICATIONS**




STRATEGIES ANDAPPROACHES


solutions

ACCURACY


The student may be unable to complete the taskwithout ongoing help; cannot follow proceduresindependently.

• may be unable to identify the basic conceptsand procedures needed to solve problems orcomplete tasks that have been modelled in class

• work is inaccurate or incomplete• may need one-to-one support to identify

simple patterns and relationships

• cannot break the task into stages, steps,or sections

• unable to verify results or solutions by usingestimation, inverse operations, or a calculator

• may include major errors in recording orcalculations (addition and subtraction to10 000; multiplication of three-digit by one-digit numbers; division of two-digit byone-digit numbers)

• work may be unclear and confusing• may omit required tables, charts, shapes, nets,

bar graphs, pictographs; those provided may beinappropriate, inaccurate, or incomplete

• may be unable to explain procedures andresults; often illogical

The work satisfies most basic requirements of thetask, but it is flawed or incomplete in some way. Thestudent may need some help.

• identifies some of the concepts and proceduresneeded to solve problems or complete tasks thathave been modelled in class

• applies most relevant mathematical concepts andskills appropriately; work is incomplete or includessome errors

• identifies simple patterns and relationships;may need help seeing how to use them(e.g., to make predictions)

• attempts to follow instructions; does not check oradjust procedures

• needs help to use estimation, inverse operations,or a calculator to verify results or solutions

• may include some recording or calculation errors(addition and subtraction to 10 000; multiplicationof three-digit by one-digit numbers; division oftwo-digit by one-digit numbers); comparisons aregenerally reasonable

• work may be confusing in places• includes most required tables, charts, shapes, nets,

bar graphs, and pictographs, but may beincomplete or include some errors

• explanations and conclusions may be incomplete;includes little mathematical language

The work is complete and accurate (may include minor flawsor errors). The student is able to develop a simple extensionof the same mathematical idea.

• identifies concepts and procedures needed to solveproblems or complete tasks that have been modelledin class

• applies relevant mathematical concepts and skillsappropriately; may be somewhat inefficient or make minorerrors or omissions

• identifies, explains, and uses patterns and relationships(e.g., to make predictions)

• structures the task logically, breaking it into steps or stages,but may be inefficient

• if asked, verifies results or solutions by using estimation,inverse operations, or a calculator

• recording and calculations are generally accurate,including units; may include minor errors (addition andsubtraction to 10 000; multiplication of three-digit by one-digit numbers; division of two-digit by one-digit numbers)

• work is generally clear and easy to follow; may besomewhat untidy in places

• required tables, charts, diagrams, or graphs are generallyaccurate, including labels and titles; may have minor errorsor omissions, particularly in more complex tasks

• offers logical explanations and conclusions; uses somemathematical language (e.g., added up, estimated, equal)

The work is complete, accurate, and efficient. The studentmay find an alternative or shortcut, or develop anextension or additional application of the samemathematical idea.

• identifies concepts and procedures needed to solveproblems or complete tasks; may propose alternativesolutions or shortcuts that go beyond procedures modelled

• applies relevant mathematical concepts and skillsappropriately and efficiently; precise

• identifies, explains, and uses patterns and relationships(e.g., to make predictions, create shortcuts); may noticesubtle patterns

• structures the task efficiently, breaking it into logicalsteps or stages

• may independently verify results or solutions by usingestimation, inverse operations, or a calculator

• all recording and calculations are accurate, includingunits (exercise some tolerance for minor errors); may usemental math to arrive at a solution quickly

• work is clear and easy to follow• required tables, charts, diagrams, or graphs are accurate and

complete, including labels and titles (may have minor errors,particularly in more complex tasks); may voluntarily includefeatures that help to clarify the task or result

• offers logical explanations and conclusions; usesappropriate mathematical language; often detailedand insightful


• presenting work• constructing charts,

diagrams, displays• explaining

procedures, results

MONEY TASKS

• estimate, count, record collections ofcoins and bills up to $100

• purchases and change up to $100

CHANCE TASKS

• design and conduct simpleprobability experiments

• identify an outcome using termspossible, impossible, certain, uncertain

• compare outcomes using termsequally, likely, more or less likely

DATA ANALYSIS

• select appropriate sample orpopulation

• collect first- and second-hand data• create interval graphs or tables• construct bar graphs and pictographs• evaluate data collection processes

MEASUREMENT

• estimate, measure, comparequantities

• standard units: mm, cm, m, km, cm2,m2,ml, L, g, kg

• length, height, perimeter,circumference

• 24-hour clock; a.m., p.m.; years,decades, centuries, millenniums

• construct 2-D shapes, 3-D objects

* Student performance that falls within the wide range ofexpectations for Grade 4 generally matches the Level 2/3descriptions in the reference set Evaluating MathematicalDevelopment Across Curriculum.

**Some of the concepts and skills students are expected to apply incompleting numeracy tasks are specific to the type of task. Theshaded charts below the Rating Scale show some of the conceptsand skills most likely to apply in Grade 4.

OTHER APPLICATIONS OF SPACEAND SHAPE

• compare and contrast pyramidsand prisms

• identify and sort quadrilaterals• recognize and draw point, line,

parallel lines, intersecting lines

G R A D E 4 N U M E R A C Y○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○


46 47


5

Student Samples

Level of Work.

Teacher’s Observations. These are additional comments by the

teacher and key relevant criteria from the Rating Scale.

Rating Scale Icon. This is a generalized summary of the scale

completed by the teacher. Here is how the actual scale looks for

this sample:

Student Work. This shows a reproduction of the student’s work.

(Names of students and teachers have been changed where this

information could be used to identify individuals.)

G R A D E 4 N U M E R A C Y○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○

51

M E E T S E X P E C TAT I O N S ( M I N I M A L L E V E L )

Teacher’s Observations

The data collection and display meets most basic requirements of the

task, but the explanation is confusing and does not deal with the

mathematical aspects of the task.

◆ identifies some of the concepts and procedures needed

◆ applies most relevant mathematical concepts and skillsappropriately; work is incomplete

◆ required tables and graphs are generally accurate

◆ explanations and conclusions are incomplete

ExceedsNot Yet Meets Fully

SNAPSHOT

CONCEPTS

STRATEGIES

ACCURACY

REPRESENTATION

Fully Meets Expectations Exceeds ExpectationsAspect Not Yet Within Expectations Meets Expectations (Minimal Level)

Rating Scale: Grade 4 NumeracyThese criteria may apply at any time of the year, depending when specific skills or concepts are introduced. *

SNAPSHOT

CONCEPTS ANDAPPLICATIONS**




STRATEGIES ANDAPPROACHES


solutions

ACCURACY


The student may be unable to complete the taskwithout ongoing help; cannot follow proceduresindependently.

• may be unable to identify the basic conceptsand procedures needed to solve problems orcomplete tasks that have been modelled in class

• work is inaccurate or incomplete• may need one-to-one support to identify

simple patterns and relationships

• cannot break the task into stages, steps,or sections

• unable to verify results or solutions by usingestimation, inverse operations, or a calculator

• may include major errors in recording orcalculations (addition and subtraction to10 000; multiplication of three-digit by one-digit numbers; division of two-digit byone-digit numbers)

• work may be unclear and confusing• may omit required tables, charts, shapes, nets,

bar graphs, pictographs; those provided may beinappropriate, inaccurate, or incomplete

• may be unable to explain procedures andresults; often illogical

The work satisfies most basic requirements of thetask, but it is flawed or incomplete in some way. Thestudent may need some help.

• identifies some of the concepts and proceduresneeded to solve problems or complete tasks thathave been modelled in class

• applies most relevant mathematical concepts andskills appropriately; work is incomplete or includessome errors

• identifies simple patterns and relationships;may need help seeing how to use them(e.g., to make predictions)

• attempts to follow instructions; does not check oradjust procedures

• needs help to use estimation, inverse operations,or a calculator to verify results or solutions

• may include some recording or calculation errors(addition and subtraction to 10 000; multiplicationof three-digit by one-digit numbers; division oftwo-digit by one-digit numbers); comparisons aregenerally reasonable

• work may be confusing in places• includes most required tables, charts, shapes, nets,

bar graphs, and pictographs, but may beincomplete or include some errors

• explanations and conclusions may be incomplete;includes little mathematical language

The work is complete and accurate (may include minor flawsor errors). The student is able to develop a simple extensionof the same mathematical idea.

• identifies concepts and procedures needed to solveproblems or complete tasks that have been modelledin class

• applies relevant mathematical concepts and skillsappropriately; may be somewhat inefficient or make minorerrors or omissions

• identifies, explains, and uses patterns and relationships(e.g., to make predictions)

• structures the task logically, breaking it into steps or stages,but may be inefficient

• if asked, verifies results or solutions by using estimation,inverse operations, or a calculator

• recording and calculations are generally accurate,including units; may include minor errors (addition andsubtraction to 10 000; multiplication of three-digit by one-digit numbers; division of two-digit by one-digit numbers)

• work is generally clear and easy to follow; may besomewhat untidy in places

• required tables, charts, diagrams, or graphs are generallyaccurate, including labels and titles; may have minor errorsor omissions, particularly in more complex tasks

• offers logical explanations and conclusions; uses somemathematical language (e.g., added up, estimated, equal)

The work is complete, accurate, and efficient. The studentmay find an alternative or shortcut, or develop anextension or additional application of the samemathematical idea.

• identifies concepts and procedures needed to solveproblems or complete tasks; may propose alternativesolutions or shortcuts that go beyond procedures modelled

• applies relevant mathematical concepts and skillsappropriately and efficiently; precise

• identifies, explains, and uses patterns and relationships(e.g., to make predictions, create shortcuts); may noticesubtle patterns

• structures the task efficiently, breaking it into logicalsteps or stages

• may independently verify results or solutions by usingestimation, inverse operations, or a calculator

• all recording and calculations are accurate, includingunits (exercise some tolerance for minor errors); may usemental math to arrive at a solution quickly

• work is clear and easy to follow• required tables, charts, diagrams, or graphs are accurate and

complete, including labels and titles (may have minor errors,particularly in more complex tasks); may voluntarily includefeatures that help to clarify the task or result

• offers logical explanations and conclusions; usesappropriate mathematical language; often detailedand insightful


• presenting work• constructing charts,

diagrams, displays• explaining

procedures, results

MONEY TASKS

• estimate, count, record collections ofcoins and bills up to $100

• purchases and change up to $100

CHANCE TASKS

• design and conduct simpleprobability experiments

• identify an outcome using termspossible, impossible, certain, uncertain

• compare outcomes using termsequally, likely, more or less likely

DATA ANALYSIS

• select appropriate sample orpopulation

• collect first- and second-hand data• create interval graphs or tables• construct bar graphs and pictographs• evaluate data collection processes

MEASUREMENT

• estimate, measure, comparequantities

• standard units: mm, cm, m, km, cm2,m2,ml, L, g, kg

• length, height, perimeter,circumference

• 24-hour clock; a.m., p.m.; years,decades, centuries, millenniums

• construct 2-D shapes, 3-D objects

* Student performance that falls within the wide range ofexpectations for Grade 4 generally matches the Level 2/3descriptions in the reference set Evaluating MathematicalDevelopment Across Curriculum.

**Some of the concepts and skills students are expected to apply incompleting numeracy tasks are specific to the type of task. Theshaded charts below the Rating Scale show some of the conceptsand skills most likely to apply in Grade 4.

OTHER APPLICATIONS OF SPACEAND SHAPE

• compare and contrast pyramidsand prisms

• identify and sort quadrilaterals• recognize and draw point, line,

parallel lines, intersecting lines

4

3

1

2

4

3

1

2

For each taskthere is oneexample ofstudent workat each of thefour levels.


6

The BCperformance

standards cancontribute to a

comprehensiveassessment and

evaluationsystem.

Using the Standards

T eachers use a variety of methods to gather the information they

need to assess, evaluate, and report on student learning.

Possible methods include classroom and standardized tests,

observations, student work portfolios, conferences, self- and peer

assessment, and performance tasks.

The BC performance standards give teachers a way to assess students’

abilities to apply their learning in realistic performance tasks in the areas

of reading, writing, numeracy and social responsibility. Used with other

methods, they can be an important part of a comprehensive assessment

and evaluation system. The standards:

◆ should be used within the context of ongoing classroominstruction. They are meant to be curriculum-embedded—used aspart of regular classroom learning activities.

◆ provide resources for assessing and evaluating the quality of aspecific piece or a collection of student work from various subjectareas. They can help to develop a profile of student achievement,typically based on three to seven pieces of work.

◆ assume that in most cases teachers are observing students as theywork. Often, some of the evidence needed to make decisions abouta student’s work comes from observations and conversations withstudents.

◆ allow for teachers to intervene where students are unable tocomplete a task independently. The level of assistance required isoften one of the criteria for determining whether or not a student’swork falls within grade-level expectations.

◆ may be adapted as needed. This might mean creating scales forgrades not included in the standards, developing IEPs or othertailored evaluation, or adjusting expectations for different timesof the year.


7

The BCperformancestandards canbe used to helpplan instruction.

Supporting Learning

T he BC performance standards are intended to support

instructional decision-making. Teachers may want to consider

the following questions as they plan instruction:

◆ How do these standards match my/our expectations for students atthis level?

◆ What kinds of instructional strategies and learning opportunitieswill help most students develop the skills they need to meet theseexpectations?

◆ What additional support and interventions will be needed to helpall students meet these expectations?

◆ If there are some students for whom these expectations are notappropriate, what expectations should they meet?

◆ What evidence do I/we need to collect to find out if students aremaking progress towards the expectations?

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Numeracy in BC Schools

Numeracy refers to the application of mathematical

understanding in daily activities at school, at home, at work,

and in the community. It involves both using mathematical

skills and knowing how mathematics can be used to solve problems.

Just as there is more to literacy than teaching the rules and procedures

of language, there is more to numeracy than teaching the rules and

procedures of mathematics. Numerate individuals not only “know”

mathematics, but understand it in personally meaningful terms. They

feel competent and confident about their ability to draw on the

necessary knowledge and apply it in new and relevant ways.

Numeracy and Mathematics

Numeracy as a skill area is currently evolving in the BC school

system. The following is the understanding of the term as it is

used in this document. This may be refined and adjusted as our

understanding improves.

Numeracy involves concrete applications in which students, confidently

and independently, use mathematics to address real tasks or problems

in an increasing variety of situations. The ability to recognize the

mathematical demands and possibilities in a situation is an important

aspect of numeracy.

Numeracy is based on mathematical foundations and requires the

application of concepts and skills related to the formal aspects of the

discipline of mathematics. These formal aspects are reflected in the

organizers for BC mathematics curricula:

◆ Number (Concepts and Operations)

◆ Patterns and Relations

◆ Shape and Space

◆ Statistics and Probability

◆ Problem Solving (Grades 8-12)

Numeracy tasks and problems typically draw on concepts and skills

from two or more of the curriculum organizers listed above, and can


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be grouped according to purpose or context. For example, Human

Resources Development Canada describes numeracy as an essential skill

and identifies five contexts or applications in which adults are required

to apply mathematical concepts and skills in the workplace:

◆ money math

◆ scheduling or budgeting and accounting math

◆ measurement and calculation math

◆ data analysis math (including chance)

◆ numerical estimation

Part of a Comprehensive Picture

The BC performance standards for numeracy can be used to evaluate

students’ abilities to use the mathematics they have learned to

address concrete, practical, and age-appropriate tasks and problems. The

performance standards do not address all aspects of the mathematics

curricula and need to be used in combination with other forms of

assessment to develop a comprehensive picture of student achievement

in the BC mathematics curricula.

Although this document currently includes only grades 1 through 8,

it is the intention that numeracy be a focus in BC classrooms from

Kindergarten to Senior Secondary. Work is ongoing in this area.

Curriculum Connection

In BC schools, primary responsibility for developing and evaluating

mathematical skills is assigned to mathematics. Depending on the

tasks developed or selected, using the numeracy standards can help

teachers address a wide range of outcomes from the provincial

mathematics curricula.

However, students are expected to apply and extend their numeracy

skills in a variety of content areas (e.g., map reading/making in social

studies; constructing/interpreting data tables and graphs in science; data

analysis and evaluation in areas such as history, English language arts,

and career and personal planning; tracking progress in physical education;

using perspective in visual arts). The performance standards for numeracy

have therefore also been developed to apply in all curriculum areas.

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Aspects of Numeracy

The performance standards focus on four aspects of numeracy, as

described here.

C O N C E P T S A N D A P P L I C AT I O N S

◆ recognizing the mathematical demands and possibilities in asituation or task

◆ applying grade-specific concepts and skills

◆ recognizing and using patterns and relationships

Evidence comes from observing and talking to students and analyzing

their work. In school, many numeracy tasks simulate real applications

(rather than having students find problems to solve on their own) and

thus do not provide evidence of ability to recognize the mathematical

possibilities in a situation.

S T R AT E G I E S A N D A P P R OAC H E S

◆ structuring the task into logical steps or stages

◆ verifying solutions

Evidence comes from observing and talking to students and analyzing

their work. With younger students, most evidence comes from

observation. Older students may clearly demonstrate these features in

their written work if the task is structured to require it.

A C C U R A C Y

◆ recording and calculations

Evidence comes from examining student work.

R E P R E S E N TAT I O N A N D C O M M U N I C AT I O N

◆ presenting work

◆ constructing charts, tables, diagrams, and displays

◆ explaining procedures and results

Evidence of presentation and construction comes from examining

student work. It is usually necessary to prompt students to specifically

explain procedures and results. Evidence of this aspect is most effectively

gathered through conferences; however, students can also provide

written explanations.

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